The present invention is related to the field of scattering (or "S") parameter measurement instruments, such as a vector network analyzer (or "VNA"). In particular, a novel calibration methodology for such instruments is disclosed that minimizes the number of calibration steps required to fully calibrate the measurement instrument so that the S parameters of a multi-port device under test (or "DUT") can be accurately measured. A multi-port device is characterized by its number of ports, referred to throughout this application as n, where n is 2 or greater.
In the RF and microwave regions virtually all devices are characterized by their S (or scattering) matrices. The S matrix is composed of a plurality of S parameters. S parameters are the standard method for device characterization over a very wide range of frequencies, from less than 1 MHz to above 40 GHz. These parameters are used because they are easily determined, they provide directly relevant measures of device performance, and they are well defined for any type of device. If other device representations are required, such as impedance or admittance parameters, then these can be readily deduced from the measured S parameters.
A large number of commercial test systems are available for S parameter measurement. Such systems are generally referred to as network analyzers. These instruments fall into two classes: scalar and vector. Scalar analyzers determine the amplitudes of the S parameters only, whereas vector analyzers (or VNAs) determine both the amplitudes and the phases. Scalar analyzers are far less flexible and far less accurate than vector analyzers, and are only employed in low-grade applications where equipment cost is a driving factor. Although the present system and method is generally applicable to VNA test instruments, the teaching of this application may also apply to other types of instruments that characterize S parameters (or other equivalent measurements) for a multi-port DUT.
Commercial vector network analyzers (VNAs) are typically designed to measure two-port devices, although some one-port systems are available. These types of VNA systems include a signal generator and a combination of splitters and directional couplers that connect the two measurement ports of the VNA (Port 1 and Port 2) to its amplitude and phase detection circuitry (samplers). Typical VNAs have three or four samplers, the number of samplers affecting the accuracy and cost of the instrument.
A typical device to be characterized by such a VNA may have two or more ports, typically with coaxial or waveguide interfaces. For an n-port system the S matrix (n.times.n) is defined by: EQU b=Sa, (1)
where a is an n-component vector containing the amplitudes of the waves incident on the device ports, and b is a vector containing the amplitudes of the outgoing waves. More formally, the wave amplitudes are defined by: EQU a.sub.i =(V.sub.i +Z.sub.i I.sub.i)/2, (2) EQU b.sub.i =(V.sub.i -Z.sub.i I.sub.i)/2, (3)
where a.sub.i is the incident voltage wave amplitude, b.sub.i is the outgoing voltage wave amplitude, V.sub.i is the voltage, I.sub.i is the input current, and Z.sub.i is the normalizing impedance, all for the i'th port under test.
The port-normalizing impedances (Z.sub.i) are typically chosen to be equal to the characteristic impedances of the coaxial cables in the test system, which are 50 .OMEGA. inmost cases. If a given port is terminated with its normalizing impedance (a matched load) then the incident wave amplitude at that port is identically zero (from equation (2)).
When a device is connected to the test ports of a network analyzer, a signal is applied to each device port in succession, and the reflected and transmitted waves are detected with the aid of the directional couplers. The S parameters for the device are then deduced by measuring the amplitude and phase of each of these waves relative to those of the input signal.
In practice, there are inevitable hardware imperfections in any VNA test system, which are principally related to port mismatch, coupler directivity, and instrument frequency response. Without correction, these imperfections can produce significant measurement errors. The error correction procedure now universally employed was first introduced approximately 30 years ago, and it differed from earlier techniques in that it relied on software data processing rather than hardware adjustments. This procedure is described in detail in R. A. Hackborn, An Automatic Network Analyzer System, Microwave Journal, pp 45-52, May 1968, and J. Fitzpatrick, Error Models for Systems Measurement, Microwave Journal, pp 63-66, May 1978.
The basic concept in this known procedure is to use a mathematical model of the test system, with a certain number of unknown terms (usually 12), which describe all of the main error contributions. Initially, a sequence of measurements is performed on a set of calibration components with accurately known S parameters. The values of the unknown model terms can be determined from these measurements, and the model can then be used to eliminate errors from subsequent device measurements. After correction, the device S parameters have an accuracy comparable to that of the original calibration components despite any imperfections in the test hardware.
Many DUTs have more than two electrical ports. However, they must also be measured with two-port VNAs. To accommodate the multi-port DUT with a two-port VNA, the simplest procedure is to make measurements between two ports, e.g., i and j, with the other ports terminated with accurate loads. This serves to determine the S.sub.ii, S.sub.ij, S.sub.ji and S.sub.jj terms in the n.times.n S matrix. And by repeating this procedure for all n(n-1)/2 possible pairs of ports, the full S matrix for the multi-port device can be determined.
This procedure has many disadvantages, however, such as: (1) a large number of separate measurements must be made, with the hardware being reconfigured at each stage; (2) it assumes that accurate terminations are available, which may not be true at all frequencies; and (3) reconfiguration of the hardware between measurements is impractical when components are being tested in thermal or thermal vacuum (TVAC) chambers. Because of these disadvantages, as well as others, full characterization of a multi-port device (particularly for large n) is rarely done.
For these reasons, multi-port testing often employs special programmable switch boxes, which are also commercially available. The switch box contains at least as many test ports as there are electrical ports on the DUT. Any test port on the switch box can be connected to either port of the two-port analyzer. In operation, two test ports are usually active, and are coupled to the analyzer, and the remainder are terminated in the switch box. When a device is connected to the test setup, any of the transmission paths can be measured automatically without reconfiguring the hardware. This greatly speeds up measurements, and allows testing to be performed in thermal or TVAC chambers. In such testing, only the DUT is placed in the chamber. The test equipment remains outside, and the test cables that connect the switch box to the DUT are routed into the chamber via special feedthroughs.
The use of a programmable multi-port switch box is not, however, without its problems. Every transmission path through the switch box that is used for measurements must first be calibrated. Calibrating such a large number of paths is very time consuming, and requires exceptional care on the part of the operator. The use of the wrong calibration component at any stage in this procedure will completely invalidate subsequent measurements. In addition, because the unused test ports are terminated in the switch box at the far end of the test cables, the loads presented to the DUT are relatively inaccurate. The resulting load mismatches can introduce significant errors into the S parameter measurements.
For this type of test setup, the determination of even one corrected S parameter requires the measurement of all the S parameters. For example, consider a 17-port device, i.e., n=17. For such a device, 136 two-port measurements would be required [n(n-1)/2=(17.times.16/2)] to determine any corrected S parameter. Making the switch box measurements is not a great problem, but calibrating the measurement system across all possible paths is extremely difficult, particularly as n becomes large, as in this example. Such a calibration task is hopelessly time consuming and error prone. In addition, this task is difficult because it is frequently necessary to use semi-rigid test cables, due to their stability, and it is not practical to make transmission measurements between all possible pairs of ports without an excessive amount of cable bending. Thus, at present, full n-port error correction is not commercially practiced.
Because of these problems, calibrating an S parameter measurement system for a multi-port DUT at present typically involves calibrations only across the test paths required for measuring the most important S parameters (typically n paths are required). This is known as a "partial" calibration. In this type of calibration, the more important S parameters are measured and the mismatch errors are simply tolerated.
Thus, there remains a general need in this field for an S parameter calibration system and method in which the number of full calibrations required to accurately characterize the S parameters for a multi-port device is reduced to a minimum.